In the early ‘70s, the Black-Scholes model ([1]}) put the pricing of options on a rigorous conceptual and mathematical basis. Assuming that the underlying asset volatility is constant was a reasonable simplification to make, and indeed, it was a good approximation for equity markets before the 1987 Black Monday crash. Since then the empirical observation is that options at different strike prices (K) imply different volatilities. This behaviour of the market is called the volatility skew or volatility smile. During the ‘90s several local volatility models appeared which were the generalisation of Black-Scholes and tried to capture the observed volatility smile (such as [2]}, [3]}, [4]}). While these models could well reproduce the static pattern of the smiles they were unable to predict their dynamics. An effective solution to this problem was provided by stochastic volatility models ([5]}, [6]}, [7]}). One frequently used approach proposed by Hagan and coworkers is the SABR stochastic volatility model ([8]}). SABR uses two coupled stochastic differential equations to describe the time development of the underlying asset price and its volatility. However, the dynamics of the volatility smile is still not described properly by the SABR model either. Traders have to recalibrate relatively often the \(\rho \)  and \(\nu \)  SABR parameters to fit the model to the observed data. As in the case of many fields of science, models used in the financial industry also became more and more complicated, having larger and larger degrees of freedom to better describe a specific problem. The usual model development process consists of two main steps: 1) Find the most relevant parameters of the problem and create a mathematical model that describes the relation between them; 2) Compare the model behaviour with the observations, and go back to step 1 if there is a non-negligible discrepancy. This clearly shows that during this iterative process it is really hard to find the number of minimally required parameters and the correct relations among them.
